Mass of a sphere, checking my result

Let be a ball with radius and in which the density of any point is equal to the distance to a fixed diameter. Find the mass of the ball.

My attempt : .
I had a hard time finding that if I chose the fixed diameter as the -axis. Then I simply converted into spherical coordinates chosing " " instead of " " because I already got confused in another exercise because of the notation.
Is my result correct?